Question

What is (9 − 2)^2)^4 / (4 + 3)^5 written in simplest form?

Answer 1

Answer:

 $\frac{[(9-2)^{2}]^{4}}{(4+3)^{5} }$ = 7³

Step-by-step explanation:

Let us revise some rules of exponents

• $a^{m}*a^{n}=a^{m+n}$

• $\frac{a^{m}}{a^{n}}=a^{m-n}$

• $(a^{m})^{n}=a^{mn}$

Let us use some of these rules to solve the question

∵ The expression is $\frac{[(9-2)^{2}]^{4}}{(4+3)^{5} }$

→ At first, simplify the bracket

∵ 9 - 2 = 7 and 4 + 3 = 7

∴  $\frac{[(9-2)^{2}]^{4}}{(4+3)^{5} }$ = $\frac{[(7)^{2}]^{4}}{(7)^{5} }$

→ Use the 3rd rule above to simplify the numerator

∵ $(7^{2})^{4}=7^{(2)(4)}$

∴  $\frac{[(7)^{2}]^{4}}{(7)^{5} }$ =  $\frac{7^{8}}{7^{5}}$

→ Use the 2nd rule above to simplify the result

∴  $\frac{7^{8}}{7^{5}}$ = $7^{8-5}$ = 7³

∴  $\frac{[(9-2)^{2}]^{4}}{(4+3)^{5} }$ = 7³